Presentation at 6th EUROPEAN CONGRESS ON COMPUTATIONAL METHODS IN APPLIED SCIENCES AND ENGINEERING, the University of Vienna, Austria

1. 1
6th EUROPEAN CONGRESS ON COMPUTATIONAL METHODS IN APPLIED SCIENCES AND
ENGINEERING, the University of Vienna, Austria, September 10-14, 2012.
MULTI-DISCIPLINARY CONCEPTUAL DESIGN OF
MULTI-STAGE HYBRID ROCKET USING GENETIC
ALGORITHM AND DATA MINING TECHNIQUE
○Masahiro Kanazaki
Tokyo Metropolitan University
Yosuke Kitagawa
Tokyo Metropolitan University
Koki Kitagawa
Japan Aerospace Exploration Agency
Masaki Nakamiya
Kyoto University
Toru Shimada
Japan Aerospace Exploration Agency

2. 2
Contents
• Background
• Objectives
• Design methods
– Evaluation procedure of hybrid rocket engine (HRE)
– Multi-objective Genetic Algorithm (MOGA)
– Analysis of Variance (ANOVA)
– Self-organizing Map (SOM)
• Formulation (Design problem for LV with HRE)
– Design variables
– Objective functions
• Results
– Design and visualization results
– Design knowledge
• Conclusions

3. 3
Background
 Rockets presently used for space
transportation
 Solid-propellant rocket engine
Advantage：・Simple mechanism and construction
・Easy to maintain the propellant
Disadvantage：・Inability to stop combustion after it is ignited
・Low specific impulse (Isp)
・Environment issues
(caused by ammonium perchlorate (NH4ClO4),
and aluminum oxide (Al2O3))
 Liquid-propellant rocket engine
Advantage ： ・Ability to stop/restart combustion
・High specific impulse (Isp)
Disadvantage：・Complex mechanism and construction
・Difficulty to store low temperature propellant
・Risk of explosion

4. 4
Background
 What is hybrid rocket?
• Hybrid Rocket Engine(HRE) ：
propellant stored in two kinds of phases
It can adopt the beneficial features of both the liquid
and solid rockets. SpaceShipTwo
Advantage of HRE
 Simple construction and mechanism
 Ability to stop/restart combustion
 Lower cost
HEAT-II
 Expectation for private space transportation
 Virgin Galactic：SpaceShipTwo
 Copenhagen Suborbitals ：HEAT-II for “TychoBrahe” launching
⇒HRE are introduced.
 Research working group in ISAS/JAXA.
→Plan of ground test for 5kN class HRE.

5. 5
Background
HRE research working group (HRErWG)
・Mainly single port type fuel
rport (t )  a  Goxi t 
・Several studies are carried out.
n
(combustion, measurement, simulation,
and design optimization)
fuel
rport (t )  a  Goxi t 
 n

Important empirical expression for several combustion
techniques.
rport (t )  a  Goxi t 
 n
Index n and coefficient a are empirically summarized for each
combustion techniques.
・Swirling oxidizer type HRE with polypropylene fuel
・Glycidyl Azide Polymer(GAP) fuel
rport (tfuel a  Goxi t 

・WAX (paraffin) ) n

6. 6
Background
 Difficulty of hybrid rocket design
 Solid rocket：Preliminary mixed solid propellant
 Liquid rocket：Control of mass flow of fluid propellant
→ Easy to maintain a constant oxidizer massand fuel
mass ratio (O/F) and to get a stable thrust
 HRE：The mixture of fuel and oxidizer is initiated after ignition.
Combustion occurs in the boundary layer diffusion flame.
→ Because O/F is decided in this part of combustion process, the solid fuel
geometry and the supply control of the oxidizer have to be optimally combined.
⇔With too much mass flow of oxidizer, the
rocket achieves higher thrust, but structural
weight should be heavier .
Importance to find optimum fuel geometry and oxidizer supply
⇒Multi-disciplinary design which is considered propulsion,
structure and trajectory

7. 7
Objectives
• Development of the evaluation tool for conceptual
design of launch vehicle (LV) with HRE
– Evaluation based on the empirical model
• Multi-disciplinary design exploration for concept of
three stage LV
– Solutions of multi-objective problem obtained by MOGA
– Knowledge discovery using data mining

8. 8
Flow chart of HRE evaluation
Calculation of engine specifications
- fuel size, time variation of O/F, Design variables
pressure of combustion chamber, etc.. ・ Initial value of oxidizer mass flow
・Initial value of O/F
Estimation of structural weight ・Coefficient a of regression rate
・Combustion chamber, Oxidizer tank, ・Initial value of mass flux of oxidizer
Pressurizing tank, nozzle ・Combustion time
・ Initial pressure of combustion chamber
・ Initial pressure of pressurizing tank
Engine specifications ・Aperture ratio of nozzle
Thrust by NASA-CEA* *NASA Chemical Equilibrium with Applications
(Gordon, S., et al, “Computer Program for Calculation
of Complex Chemical Equilibrium Compositions and
Trajectory Applications I. Analysis,” NASA RP-1311, 1994.)
No Kosugi, Y., Oyama, A., Fujii, K., and Kanazaki, M.: Multidisciplinary
t>combustion time？
and Multi-objective Design Exploration Methodology for Conceptual
Yes Design of a Hybrid Rocket, AIAA 2011-1634a, 2011.
Altitude, velocity, .. after mth stage combustion

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Flight Sequence
Ignition of 3rd stage
Separation of 2nd stage
Coasting
Target altitude
(perigee 250km)
Separation
of 1st stage
Launch

10. 10
Design exploration
 Heuristic search：Multi-objective genetic algorithm
(MOGA)
 Inspired by evolution of life
 Selection, crossover, mutation
 Searching global non-dominated
 NSGA2 is employed.
 BLX0.5 for cross over
Arbitral evaluation
Minimize f1
Minimize f2
Ranking by NSGA2 Crossover (BLX-α)
Flowchart of GA

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Design methods
Knowledge management1
Integrate
Analysis of Variance
One of multi-valiate analysis for quantitative information
The main effect of design variable xi:
i ( xi )     y( x1 ,....., xn )dx1 ,..., dxi 1 , dxi 1 ,.., dxn  
ˆ
variance
where:
     y( x1 ,....., xn )dx1 ,....., dxn
ˆ
μ1
Total proportion to the total variance:
 i  xi  dxi
2
pi 
  y ( x1 ,....,xn )   dx1 ...dxn
2
  ˆ
where, εis the variance due to design variable xi.
Proportion (Main effect)

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Design methods
Knowledge management2
Self-organizing map for qualititative information
– Proposed by Prof. Kohonen
– Unsupervised learning
– Nonlinear projection algorithm from high to two dimensional map
Design-objective
Multi-objective Each cell represents vector which has
same number of components as input.
Two-dimensional map
（Colored by an component, N component plane, for N
dimensional input.）
Multi-dimensional data *modeFrontier ®v4.0 is used.

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Design space
a can control by changing intensity of the oxidizer swirling.*( r  a  Gon )

* Hikone,S., et al, “Regression Rate Characteristics and Combustion Mechanism of Some Hybrid Rocket Fuels ,”Asian Joint Conference on
Propulsion and Power 2010.

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Design Problem
 Design target: Design of three-stage rocket which can deliver micro-satellites
to the Sun-synchronous orbit (SSO) (perigee is 250km, apogee is 800km)
 Objective functions
• maximize Payload mass/Gross mass (Mpay/Mtot)
• minimize Gross mass (Mtot)
 Constraints
• After combustion of third stage,
 Height > 250km
 Angular momentum > 52413.5km2/s
 -0.5deg. < Flight path angle < 0.5deg.
• Rocket aspect ratio < 20
• Radius of nozzle exit < Radius of rocket
• Area of grain port > 2・(Area of nozzle throat)
 Combustion type
• Swirling oxidizer type engine
• Oxidizer：LOX, Fuel：WAX (FT-0070)

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Result
MOGA exploration
Optimum direction
• Trade-off between objective functions
• Mpay/Mtot of “Epsilon rocket” planed by JAXA is about 1.3%
⇒Lower cost than existent LVs

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Selected Design from Non-dominated Solutions
 Selected rocket size
Length of rocket [m] 20.8
Diameter of rocket [m] 1.46
Aspect ratio of rocket [-] 14.3
1st stage 2nd stage 3rd stage
Length [m] 8.22 6.57 6.06
Diameter [m] 1.45 1.46 1.07
Gross mass [ton] 8.07 4.09 0.70
Structural mass [ton] 1.78 0.49 0.10
Structural mass ratio [%] 22.1 11.9 14.5
20.8
8.22 6.57 6.06
1.35 1.36 0.97
1.46
What kind of design can be high performance?
1.21 2.18 3.21 1.61 2.29 1.06 2.11 1.11 2.06 0.35 0.99 0.64 2.02
⇒Design knowledge discovery by means of data mining

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Knowledge discovery
Contribution ratio estimated by analysis of variance
Mtot Mpay/Mtot
• dv1, 9 (oxidizer mass flow ratios of 1st and 2nd stages) influence on Mtot.
• dv6, 14 (combustion pressure of 1st and 2nd stages) influence on Mpay/Mtot.
• dv1, 9, 17 (oxidizer mass flow ratios of all stages) influence on Mpay/Mtot.
– dv17 (oxidizer mass flow ratio of 3rd stage) remarkably influences on Mpay/Mtot.
⇒ Design of the engine for 3rd stage is important for low cost rocket.

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Knowledge discovery
• SOM visualization
• Trade-off between Mpay/Mtot and Mtot
• LV which can deriver high Mpay can not
always achieve high Mpay.
– Mpay maximization is not always explore high
efficient LV.

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Knowledge discovery
• Selection of design variables based on similarity of SOMs’ colored
map and contribution ratios by ANOVA.
• dv3, 11, 19 (coefficient a of regression rate) are also checked.
r 0  a  Go 0
 n

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Knowledge discovery
• Comparison among objective functions and design variables
dv5 dv6
dv1
2.420
139.5 56.01
To obtain higher Mpay/Mtot
60.4 46.01 1.900
• Moderate value of dv5(Combustion time of 1st stage)
dv9
dv14
1.600
dv17
3.677
18.30
• Smaller dv6, 14 (Pressure of combustion chamber of 1st and 2nd stage)
• Moderate value of dv1（Oxidizer mass flow of 1st stage）
• Larger dv9, 17(Oxidizer mass flow of 2nd and 3rd stage)
1.215 1.710
9.36

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Knowledge discovery
• Coefficient a of regression rate
r 0  a  Go 0
 n
To obtain higher Mpay/Mtot
• Lower regression rate at 1st stage
• Moderate a at 2nd stage
• Higher regression rate at 3rd stage

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Conclusions
Design exploration of multi-stage launch vehicle with
hybrid rocket engines
 Empirical expression based evaluation of HRE
• Engine size, Thrust, Structure, and Flight
 Global Exploration employing MOGA
• Type of HRE using FT0070 fuel with swirling oxidizer for all stages
• Trade-off between total mass ratio and payload-total mass ratio
 Design knowledge using ANOVA and SOM
• Oxidizer mass flow of 1st and 2nd stages have predominant effect to
total mass.
• Pressure of combustion chamber of 1st and 2nd stages influence on
payload-total mass ratio
• Knowledge about what kind of engine design is promising for each stage.
 Further study: Design exploration of LV which has different fuel in
each stage to found out better solution.

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Acknowledgement
• We thank members of the hybrid rocket engine
research working group in ISAS/JAXA for giving
their experimental data and their valuable
advices. This paper and presentation was
supported by ISAS/JAXA.
Thank you very much for your kind attention.